Apparatus and method for delivery of an aerosol

ABSTRACT

An apparatus for measuring lung ventilation, comprising: a pressure device to measure volume of air flow; an aerosol-generating device that provides aerosol particles to be released at a determined point in a breathing cycle; a mouthpiece with a detector that measures the concentration of aerosol particles for a given volume during the breathing cycle; and a computing device configured to provide lung ventilation data as a function of time constants.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional Application of U.S. Ser. No.11/771,479, filed Jun. 29, 2007, which, in turn, is a DivisionalApplication of U.S. Ser. No. 10/652,561, filed Sep. 2, 2003, now U.S.Pat. No. 7,241,269, issued Jul. 10, 2007, the entire contents of whichare incorporated herein by reference in their entireties.

FIELD OF THE INVENTION

This invention relates to an apparatus and method for the delivery of anaerosol. The apparatus and method is used to identify an aerosolinhalation volume at which lung dysfunction occurs, by measuring lungventilation at specific volumes of inhalation.

BACKGROUND OF THE INVENTION

The lungs may be characterized as a mass exchanger in which oxygen isdelivered through the alveoli to blood and carbon dioxide is removedfrom the blood for exhalation. The efficiency of the lungs, in terms ofthe exchange of gaseous materials at the blood/gas interface, isdependent in-part on the ventilation of each lung. The term“ventilation” refers to the movement of or the exchange of oxygen-richair from outside the body into the lung where the air is mixed withrelatively oxygen deficient air through the course of breathing. Theventilation function of a patient's lungs can be determined andmonitored by measuring the resistance and compliance of the airways ofthe lung.

The resistance and compliance within different regions of the lungsaffect the distribution of pulmonary ventilation. The term “resistance”refers to the flow resistance due to an obstruction or a restrictionwithin a respiratory passageway to the passage or flow of a gas to andfrom the lungs. The measured unit of resistance is H₂O/(liters/see). Theterm “compliance” refers to the flexibility or elasticity of the lungsas they expand and contract during a respiratory cycle. The measuredunit of compliance is liters/(cm-H₂O). If one multiplies resistance andcompliance, the unit of time (e.g., seconds) that remains is referred toas a “time constant.” Therefore, the ventilation function of a patient'slungs can be represented by a single value, that is, the time constant.

Spirometry is one technique used to diagnose and monitor respiratorydisease. In spirometry, the patient inhales as deeply as possible, andthen exhales until all air is completely expelled from the lungs. As onecan imagine, this requires a great deal of concentration and effort bythe patient, and thus, spirometry readings largely depend on how wellthe patient is feeling and breathing on a given day. Spirometry measuresonly the flow volume of air that is inhaled and/or exhaled by thepatient. Spirometry does not measure resistance or compliance, and doesnot rely on the calculation of time constants to determine lung functionor lung ventilation. Also, spirometry is relatively insensitive formeasurements of small airways and thus has limited use for diagnosis ofrespiratory diseases in these areas of the lung such as asthma andemphysema. Consequently, spirometry is a relatively insensitivetechnique for monitoring and diagnosing the most prevalent ofrespiratory diseases.

U.S. Pat. No. 6,135,105 by Lampotang et al. describes a method ofclassifying each lung by measuring variations in pressure or flow ratesusing an invasive endotrachael tube equipped with a pressure sensor.Time constants are computed as the product of measured resistance andcompliance. However, it is known that this procedure does not accuratelyaccount for convective transport in the small airways of the lung, andthus, can result in significant errors in measurement. Consequently, theaccuracy of the resistance and compliance values, and thus, thecalculated time constants measured using this procedure arequestionable. Also, one cannot ignore the need for the endotrachael tubeand the resulting discomfort of the patient due to this invasiveprocedure.

As a result, there is a need for an apparatus and method for correctlydiagnosing and accurately monitoring respiratory disease in a patientwithout relying on the patient's ability to breath on a particular dayor without having to insert an invasive device (e.g., endotrachael tube)into the patient.

SUMMARY OF THE INVENTION

One aspect of the present invention is directed to an apparatus formeasuring lung ventilation, comprising a pressure device to measurevolume of air flow; an aerosol-generating device that provides aerosolparticles to be released at a determined point in a breathing cycle; amouthpiece with a detector that measures the concentration of aerosolparticles for a given volume during the breathing cycle; a computingdevice configured to provide lung ventilation data as a function of timeconstants; and a multi-port coupling device configured to couple thecomputing device, mouthpiece, aerosol-generating device and pressuredevice.

Another aspect of the present invention is directed to a method formeasuring lung ventilation. The method comprises: measuring pressuredata and calculating volumes of airflow of a plurality of respiratorycycles, providing a volume of penetration, providing an aerosol bolus ata determined point of the breathing cycle, measuring concentrationvalues of aerosol particles, and calculating time constants from thevolume of penetration and the measured aerosol concentration values.

Yet another aspect of the present invention is directed to determiningthe position of an obstruction in the upper region of the lungsassociated with specific volumes of air inhaled into the lung which, inturn, are associated with air traveling through certain branches in thelung which may be restricted or obstructed due to disease or injury. Themethod comprises: a.) measuring pressure data and calculating volume ofairflow of a breathing cycle; b.) providing a volume of penetration; c.)providing an aerosol bolus at a determined point of the breathing cycle;d.) measuring a concentration values of aerosol particles andcalculating time constants from the volume of penetration and themeasured aerosol concentration values; f.) repeating steps b to d usinga different volume of penetration; and g.) comparing the calculated timeconstants from at least two provided volumes of penetration.

Yet again, another aspect of the present invention is a method fordetermining aerosol particle concentrations, comprising: measuringinhaled and exhaled aerosol concentrations at discrete values of atleast one of time, volume and dimensionless volume; estimating initialvalues for intrinsic mixing on inhalation, intrinsic mixing onexhalation, effective volume of lung on inhalation, and effective volumeof lung on exhalation; minimizing the estimated initial values;determining a volume of penetration; estimating inhaled aerosolconcentration as a function of the measured inhaled aerosolconcentration and at least one of K(V) and K(t); and estimating exhaledparticle concentration as a function of the estimated inhaled aerosolconcentration and a probability that a particle exits the lung in aprovided volume.

Another aspect of the invention comprises measuring breath holding timeand the effect of that breath holding time on the particle concentrationthat is exhaled, the particle concentration being described as apercentage of the inhaled particle concentration as a function of thevolume of penetration of the aerosol.

Yet, another aspect of the invention comprises determining a totalamount or a percentage of a total amount of inhaled particulate materialthat is exhaled in the time of a given breath or in subsequent breathsafter the breath in which an aerosol is inhaled. In addition, another,another aspect of the invention comprises recognizing materials that areused to generate an aerosol.

Further, another aspect of the invention comprises determining theretention of aerosol inhaled in a single breath and exhaled over thecourse of subsequent breaths as a diagnostic indicator of asthma.

Furthermore another aspect of the invention comprises means fordetermining a total amount or a percentage of a total amount of inhaledparticulate material that is exhaled in the time of a given breath or insubsequent breaths after the breath in which an aerosol is inhaled.Moreover, another aspect of the invention comprises means forrecognizing materials that are used to generate an aerosol.

BRIEF DESCRIPTIONS OF DRAWINGS

The invention will be better understood by reference to the DetailedDescription of the Invention when taken together with the accompanyingdrawings, wherein:

FIG. 1 depicts an exemplary embodiment of the invention;

FIG. 2 depicts an exemplary representation of volume and concentrationdata;

FIG. 3 a shows a cut-away view of an exemplary mouthpiece in thenon-active position for controlling volume drift;

FIG. 3 b shows a cut-away view of the mouthpiece of FIG. 3 a in theactive position for controlling volume drift;

FIG. 3 c shows a cut-away view of the mouthpiece of FIG. 3 a forcontrolling volume drift in used by a patient;

FIG. 4 a is a top view of the two sections of an exemplary 3-way valve;

FIG. 4 b is a front view of the two sections of an exemplary 3-wayvalve;

FIG. 4 c shows an exemplary 3-way valve in the “Filling Mode”;

FIG. 4 d shows an exemplary 3-way valve in the “Delivery Mode”;

FIG. 5 shows an exemplary flow diagram for a method for predicting lungventilation;

FIG. 6 shows an exemplary flow diagram for a method for measuring lungventilation;

FIG. 7 shows an exemplary flow diagram for a method for providing avolume of penetration;

FIG. 8 shows another exemplary flow diagram for a method for providing avolume of penetration;

FIG. 9 depicts another exemplary representation of volume andconcentration data.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention is directed to an apparatus for delivering an aerosol intothe lungs of a patient. The apparatus measures lung ventilationassociated with specific volumes of air inhaled into the lung whichdelivering an aerosol into the lungs of a patient. The inhaled airpasses through certain branches in the lung, some of which may berestricted or obstructed due to disease or injury. The apparatusincludes a pressure device, a detector, an aerosol-generating device, amulti-port coupling device and a computing device. Theaerosol-generating device provides a bolus of aerosol particles to bereleased at a determined point in a breathing cycle. The computingdevice provides information on lung ventilation as a function of timeconstants. The aerosol particles are used to measure the time constantsas the aerosol particles move in and out of the lung over a plurality ofrespiratory cycles. The term “breathing cycle” is defined as the timethe patient begins to breathe through a mouthpiece of the invention tothe time the patient completes the test. A “respiratory cycle” isdefined as one inhalation-exhalation cycle. As a result, a breathingcycle includes a plurality of respiratory cycles for a patient.

The apparatus and method of the invention provides the physician as wellas the patient with the ability to effectively monitor or treat chronicrespiratory diseases irrespective of the health of the patient or howwell the patient is able to breath on a given day. Unlike spirometry, acommon technique used to diagnose and monitor respiratory disease inpatients, the patient is not required to inhale and exhale deeply toobtain ventilation test data. Instead, the patient simply breathes intoa mouthpiece of the apparatus using normal respiratory cycles. Also, themethod of the invention can be performed by the patient, and without theneed for a trained technician.

One significant advantage provided by the apparatus and methods of theinvention is that the position of an obstruction or restriction in theupper regions of the lungs (e.g., the bronchial branches) can beidentified and monitored. The apparatus and methods of the inventionprovide detailed information on the point(s) of obstruction orinflammation for a patient. The physician can monitor the progress ofthese point(s) of obstruction, and even determine if secondary points ofobstruction develop. As a result, the apparatus and methods of theinvention provide the physician with specific information on therespiratory condition for a patient.

Another significant advantage provided by the apparatus and methods ofthe invention is the localized delivery of an aerosol bolus containingan active pharmaceutical (e.g., a bronchial dilating agent) to the pointof obstruction or inflammation. Once the point(s) of obstruction areidentified in a particular patient by the invention, the activepharmaceutical is released into the air flow at the optimal point in arespiratory cycle. In this manner, the aerosolized agent is concentratedin a selected volume of air flow that will contact the point ofobstruction.

The measurement of time constants can be an important diagnostic tool. Arelatively large time constant suggests the presence of an obstructionor restriction in the lung and indicates some form of respiratorydisease or impairment of lung function. As used in the medical sense,the term “obstruction” refers to impairment such as that found inbronchitis or emphysema whereas the term “restriction” refers toimpairment such as that found in asthma. The existence of nearlyequivalent time constants for each of the pathways to the small airwaysof the lung is referred to as “homogeneous ventilation” and is wellrecognized as a characteristic of healthy individuals. In contrast,unbalanced and longer time constants can be indicative of obstructionsand restrictions and is referred to as “non-homogeneous ventilation.”

Observed differences in regional time constants is suggestive ofregional differences in convective ventilation rates. Also, informationon the severity of the obstruction(s) can be obtained from the timeconstant data. For example, patients with airway obstructions may have arelatively slow emptying of aerosol particles from bronchi compared tohealthy patients. The more time it takes for the aerosol particles toleave the lung can be an indication of the severity of the diseasedregions of the lung.

The apparatus and method of the invention provide an accurate and directmeasurement of time constants relating to the small airways. Thisinformation is not available from spirometry, and allow the physician tomore accurately diagnose and monitor respiratory diseases or impairmentsto lung function.

The apparatus of the invention measures the concentration of aerosolparticles from an aerosol bolus with respect to time or volume during abreathing cycle. For any given flow measuring time or measuring volumecan be considered an equivalent measurement of the penetration ofparticles into the lung. The aerosol particles move with the air that isinhaled and exhaled from the lung and the apparatus records theconcentration and transit time or volume required for the particles tomove into the lung and back out. In essence, the aerosol particlesfunction as microscopic markers, which by measuring their concentrationwith respect to time or volume provide the necessary ventilation datafor a patient. The release of a “pulse” or “bolus” of aerosol particlesat some determined time during the breathing cycle, particularly theinhalation step, is one method of providing such markers. The timeconstants during exhalation are plotted as a mathematical function whichcan be used to diagnose and monitor respiratory disease. The particleconcentration with respect to time (i.e., the time constants) duringexhalation from the lung is measured to provide a specific distributionfunction of the aerosol particles for each individual patient on a givenday. The time constant data can then be stored or transmitted forcomparison with data taken on a previous or future test.

Applicants envision that following an initial diagnosis by a physicianwith the apparatus of the invention, an asthmatic patient, for example,will be provided with the apparatus or variation of the apparatus tohave in the home. The patient can then on a daily, weekly or monthlybasis monitor their asthma through a self-test. The data collected fromsuch tests can then be stored and/or transmitted to the physician (e.g.,over the Internet).

One exemplary embodiment of the invention is shown in the schematic ofFIG. 1. The arrows in FIG. 1 indicate the directions air can flow ineach component of the apparatus. The dashed lines of FIG. 1 indicatestatic pressure lines, and the thin lines indicate an electronicattachment. The apparatus includes a multi-port coupling device 105 athat couples with a detector 103 a, a pressure device 107, an aerosolgenerator 106 and a computing device 109. A patient breathes through amouthpiece (not shown) that is coupled to the detector 103 a. It is tobe understood that the configuration or position of each component inrelation to the others, as shown in FIG. 1, is only one of a handful ofpossible configurations that can be used to practice the invention.

The multi-port coupling device 105 a can be used to release an aerosolbolus produced by aerosol generator 106 into the air flow that isdelivered to the patient. Alternatively, the aerosol bolus can bereleased into the air flow by the aerosol generator 106.

The aerosol generator 106 provides an aerosol bolus to be released at adetermined point in a breathing cycle. Preferably, the aerosol bolus ismixed with the air flow during inhalation of air by the patient. Theaerosol generator 106 can be any aerosol generation system known tothose of ordinary skill that generates an aerosol with a particle sizeof from 0.05 microns to 1 micron, preferably from 0.1 microns to 0.8microns, more preferably from 0.1 microns to 0.6 microns. For example,the aerosol generator can include a pressurized chamber which containsone or more substances that is to be aerosolized, and a nozzle with aselect orifice diameter and shape.

The aerosol particles can include any relatively inert material that donot tend to aggregate within the patient, such that the particle sizeremains relatively constant as the particles are inhaled and exhaledfrom the patient's lungs. In one embodiment, the aerosol particlescomprise one or more synthetic or natural oils, or a blend of naturaland synthetic oils. The synthetic oil can include one or more fattyacids or, typically a blend of fatty acids. Most preferably, the aerosolcomprises natural oil. An exemplary list of natural oils includes cornoil, canola oil, and oils derived from nuts. Neutral oils, for example,MIGLYOL, can also be used. The material used will also be labeled by anymeans of labeling known to those of ordinary skill that can berecognized electronically by the device so that no unauthorized materialis aerosolized by the device. Examples include but are not limited tosuch identification means as bar codes, magnetic strips or eproms. Suchidentification would be encoded so as to be indecipherable by ordinarymeans.

In one embodiment, the aerosol generator 106 is coupled to themulti-port coupling device 105 a so that the aerosol bolus is releasedinto a chamber of the multi-port coupling device 105 a.

In another embodiment, the aerosol generator 106 is connected to achamber of the apparatus of the invention. In either case, the apparatusof the present invention is designed to release an aerosol bolus intothe air flow at a determined point of a breathing cycle.

The detector 103 a is used to measure the concentration of aerosolparticles of a given volume in the air flow as the patient inhales andexhales. Any type of detector 103 a known to those of ordinary skillthat can measure particulate concentrations in a given volume can beused. Examples include but are not limited to light measuring devicessuch as photometers, photocells, mephelometers or photodiodes.

In one embodiment, as shown in FIG. 1, the pressure device 107 includesa filter 107 a, a pneumotachagraph 107 b, and a pressure transducer 107c. The pneumotachagraph 107 b is used in conjunction with othercomponents of the pressure measuring device 107 to determine the volumeof air flow through the apparatus of the invention. The pneumotachagraph107 b measures a pressure differential across a fine mesh screen as airflows through the screen. The measured pressure differential isconverted to an electronic signal by pressure transducer 107 c coupledto pneumotachagraph 107 b. The electronic signal can be digitized by aninterface 109 a included with computing device 109. The differentialpressure data can be integrated with respect to time with computingdevice 109 to provide a volume of air flow for a plurality ofrespiratory cycles as well as the breathing cycle. The volume of airflow data can be stored for subsequent analysis. The computing device109 will have the capability to collect, store, manipulate and displayraw data, that is, data that is directly obtained from each component ofthe apparatus, as well as data that is generated by an algorithmicmanipulation of the raw data.

The volume data collected refers to the amount of air a patient inhalesand exhales from his or her lungs for a given respiratory cycle orbreathing cycle. The apparatus of the invention has the capability toaverage the volume of air flow over any number of respiratory cycles. Asa result, the apparatus and method of the invention can obtainventilation data irrespective of the patient's respiratory condition atany given time or on any given day.

For example, the apparatus can obtain important ventilation data from anasthmatic that is experiencing extreme difficulty in breathing on aparticular day, which is not possible with spirometry. Spirometry, whichrelies on a single respiratory cycle, can only tell the physician whathe or she already knows, that is, the patient is having difficultybreathing. Also, the apparatus and method of the invention is moresuited to collecting ventilation data from pediatric patients because achild can breath normally because there is no forced or directedbreathing as required with spirometry.

The release of an aerosol bolus at a point in a breathing cycle, and thesubsequent measurement of aerosol particle concentration with time,provides the physician with information on the upper respiratory tractof a patient. The collection of volume data allows the apparatus andmethod of the invention to determine at what point the aerosol bolusshould be released into the air flow. In a preferred method of theinvention, the aerosol bolus is released into the air flow at some pointof an inhalation step of a respiratory cycle. This allows a greaterdispersion of aerosol particles in the bronchi or upper region airwaysof the lungs where the obstruction(s) resulting from asthma or emphysemaarc typically located. This is an important feature because respiratorydiseases such as asthma and emphysema affect the upper bronchi of lungs.

The measurement of time constants of aerosol particles and the amount ofaerosol retained on any given breath as the aerosol moves just pass theobstruction or restriction and out again provides a very sensitivemeasurement of lung ventilation. The apparatus of the invention thusprovides the physician with accurate and reliable information about thelocation of disease in the respiratory tract, whereas other knowntechniques such as spirometry are relatively insensitive in this regard.

A graphical representation of volume and aerosol particle concentrationdata shown in FIG. 2 describes an exemplary way in which the apparatusand method of the invention collects and analyzes data. FIG. 2 shows theaerosol particle concentration and volume data for a given inhalationand exhalation, i.e., a respiratory cycle in which an aerosol bolus isreleased into the air flow. The aerosol particle concentration isplotted as a function of time and is depicted as a dashed line. The timeT1 corresponds to the time in the respiratory cycle that the aerosolbolus is released into the air flow. The peak volume 408 of the aerosolbolus occurs at time T2. The volume of air inhaled and exhaled by thepatient is shown as the solid line. The rising portion of the volumedata 402 with positive slope designates the inhalation step of therespiratory cycle. Likewise, the falling portion of the volume data 405with a negative slope designates the exhalation step of the respiratorycycle. FIG. 2 uses arbitrary units of volume, time, and concentration todescribe the coordinate axes.

The apparatus and method of the invention can be used to measure aparticular volume of penetration V_(p). The volume of penetration isdefined as the volume of air inhaled following the release of an aerosolbolus into the airflow. To determine V_(p), the apparatus requires thatcertain volume reference points be established. These reference pointsare volume of inhalation V₁ and total volume of inhalation V_(T). Sincethe aerosol bolus has a measurable volume there are several equallyvalid reference points that can be used to determine the volume ofinhalation. The volume of inhalation is the volume at which the aerosolbolus is released and may be defined in at least one of three ways: (1)the volume at which a signal is given or received to open a valve andlet the aerosol enter the inhalation air stream; (2) the volume at whichthe concentration of particles rises above the background level by agiven amount; or (3) the volume at which the concentration of particlesrises for some specified rate for some specified period of time.

As shown in FIG. 2, V₂ is the midpoint of the aerosol bolus 408. V₂ isdefined in one of three ways: (1) the centroid of the mass of theinhaled particle concentration; (2) the midpoint volume between thestart and end volumes of the aerosol bolus ([V₁+V₃]/2); or (3) thevolume at which the peak concentration of particles occurs. V₃ isdefined as: (1) the volume at which a signal is given or received toclose a valve and stop the flow of aerosol from entering the air flow;or (2) the volume at which the aerosol concentration drops to or belowthe background level. The preferred definition of V_(I) is the midpointvolume. Further, the volume of penetration V_(P) can be expressed as thedifference between the average total volume of inhalation V_(T) and thebolus inhalation volume V_(I) (i.e., V_(P)=V_(T)−V_(I)).

As an example, in an adult asthma patient, typically it is only the last50 cm³ to 400 cm³ of inhaled volume, more typically, 50 cm³ to 200 cm³of inhaled volume, that provides the physician with importantventilation data. In a child, typically it is the last 25 cm³ to 200cm³, more typically 25 cm³ to 150 cm³, of inhaled volume. In an infant,typically it is only the last 10 cm³ to 100 cm³, more typically 10 cm³to 50 cm³ of inhaled volume. The term “adult” is defined as a personhaving reached the age of twelve. The term “child” is defined as aperson between the ages of two and twelve. The term “infant” is definedas a newborn to the age of two.

The average total volume of inhalation can be determined prior torelease of the aerosol bolus as the patient inhales and exhales througha mouthpiece of the apparatus. The digitized voltage of the pressuretransducer is integrated to yield the volume of inhalation andexhalation irrespective of the total volume airflow. The method includescalculating an average volume of inhalation for any number ofrespiratory cycles before the aerosol bolus is released into the airflow. The average volume of inhalation can be stored in data storage109. As the standard deviation of the running average of previousrecorded volumes falls within a select value, the average inhalationvolume is determined. Once the average inhalation volume is determined,the computing device 109 signals the multi-port coupling device 105 torelease the aerosol into the air flow. Alternatively, the aerosolgenerator can release the aerosol directly into the air flow.

The pressure data is integrated with respect to time by the computingdevice 109. Consequently, any electronic noise or voltage offset thatoccurs during this time results in an error that should be corrected.This error is commonly referred to as “zero signal drift” or “volumedrift”, and accounts for differences in recorded volume/time data, whichcan be negative or positive differences, even if there is no air flowpassing through the system. If this error component is significant andnot accounted for the apparatus could interpret the volume drift as airflow that occurs during a breathing cycle. This volume drift could thencause errors in the measurement of volumes, and result in incorrecttiming for the release of the aerosol bolus into the air flow.

In one embodiment, the apparatus includes a means for compensating forvolume drift. For example, the apparatus can have the capability ofdigitally adding or subtracting values to and from the pressure flowsignal from the pneumotachagraph 107 b to nullify any error due tonoise, thus maintaining a net volume drift of zero,

FIG. 3 a and FIG. 3 b show a cut-away view of an exemplary means forcontrolling volume drift in the form of a volume drift control switch201 a, 201 b. A cut-away view of a volume drift control switch that isnot activated and a volume drift control switch 201 b that is activatedis shown in FIG. 3 a and FIG. 3 b, respectively.

The apparatus of the present invention can also include a sensor switch203. The sensor switch 203 is coupled to the computing device 109, andcommunicates with computing device 109 as to initiation of a test orwhen data collection should begin. In one embodiment, a sensor switch203 a, 203 b can be installed in the volume drift control switch 201 a,201 b. For example, if the sensor switch 203 a is not activated or inthe open position, the signal from the pressure transducer 107 c is notintegrated and the volume drift remains uncorrected. However, if thesensor switch 203 b is activated or in the closed position, the signalfrom the pressure transducer 107 c is integrated to calculate volumedata and the volume drift is corrected. In one embodiment, the sensorswitch can include a toggle or button switch that remains closed as longas the switch is held in the closed position.

In another exemplary embodiment, the sensor switch 201 is a retractablecovering 205 for a mouthpiece 202, as shown in FIGS. 3 a and 3 b. InFIGS. 3 a and 3 b, the retractable covering 205 is a hollow tube open atboth ends that can be retracted exposing the mouthpiece 202 by pushingagainst the retractable covering 205. The patient's lips push againstthe retractable covering 205 while inserting the mouthpiece 202 intotheir mouth. FIG. 3 c shows an example of the volume drift controlswitch 200 with the subject 101 inserting the mouthpiece 202 into theirmouth while pushing against the retractable covering 205 and activatingthe sensor switch 203. Activation of the sensor switch 203 occurs whenthe retractable covering 205 completes a circuit 204 by closing thesensor switch 203. An audible or visual sensor indicator signal can thenbe enabled by the circuit 204 to give an audible or visual sign that thesensor switch 203 has been activated and the test can begin. Uponremoval of the mouthpiece from the mouth, a coil or spring 206 allowsthe retractable covering 205 to return to its original position.

In yet another exemplary embodiment, the sensor switch further comprisesa proximity sensor that is used to determine when to stop signalaveraging of a zero flow signal. The proximity sensor comprised of atleast an electromagnetic wave source or transmitter of any wavelengthwith a matched receiver and shall be used to determine the proximity ofa user to the aerosol dispersion device. The electromagnetic wave sourceis associated with the mouthpiece and shall transmit electromagneticwaves that shall be reflected from the body of the user back to thereceiver that is also associated to the mouthpiece. The receiver shallbe positioned at an angle of less than 90 degrees relative to the angleof the emitter. When the signal is received at the receiver, thecomputing device 109 shall cease averaging the pressure signal used todetermine flow. In a preferred embodiment, the average pressure value isdetermined for the previous five seconds, but does not count the lastsecond before the signal is received by the receiver, as the averagezero pressure value. In addition, longer or shorter durations may beused for averaging times since the value is programmable. Changes inpressures encountered as long as the receptor is receiving emissions ofelectromagnetic waves shall be considered as due to flow and shall beintegrated to determine the volume inhaled or exhaled by the user of theaerosol dispersion device. In a preferred embodiment the receiver andthe transmitter shall be positioned in close proximity to one anotherand shall be in close proximity to the face of the user when the aerosoldispersion device is being used as intended.

In yet another exemplary embodiment, the multi-port coupling device 105is a 3-way valve, as shown in FIG. 4 a. The 3-way valve 105 a is coupledto the mouthpiece with detector 103, pressure device 107, and computingdevice 109. The 3-way valve is comprised of at least two sections asshown in. FIG. 4 b.

When it is determined that an aerosol bolus needs to be injected intothe breathing stream of the patient the valve system goes into theDelivery Mode, as shown in FIG. 4 c. In this mode, the 3-way valve 3 isactuated to stop the flow of the gas into the piston chamber 4 and thevalve 3 is opened to the atmosphere so that the pressure inside thepiston chamber 4 is released. With the pressure released, the piston 5is pushed back by the action of the spring 8 against the slider section9 which slides freely against the piston. The spring 8 and the twochambers (A and B) in the slider are sized, so that the holding chamberA, filled with aerosol is positioned in the breathing stream of thepatient. While the patient continues breathing a pulse or bolus ofaerosol is delivered to the patient's lungs.

In the “Delivery Mode,” as shown in FIG. 4 c, the valve 9 acts tosafeguard the subject from an accidental exposure to large volumes ofhigh pressure gas which, if not controlled, could damage the subject'slungs. There is a double protection mechanism in this configurationbecause the holding chamber A can not be moved into the breathing streamuntil the valve 3 from the high pressure gas is closed. In addition,even if the valve 3 would fail or the pressure regulator 2 would failthe holding chamber is not connected to the pressurized portion of thesystem when the patient is breathing from it.

When in a “Filling Mode,” the 3-way valve, as shown in FIG. 4 d,consists of a gas source 1, e.g. carbon dioxide that is regulated, by apressure regulator 2 through which the gas passes to a three-way valve 3that can be actuated electronically to allow the gas to flow to a pistonchamber 4. As gas flows into the piston chamber 4, movement of piston 5provides passage of the gas into an aerosol nebulizer 6. As the gasflows into the nebulizer 6 an aerosol is generated. The generatedaerosol flows into a holding chamber A in the slider section 9 of the3-way valve, with any overflow being collected by a filter 7 which isopen to the air. The filter may be located either, as shown in FIG. 4 c,on the upstream side of the holding chamber A or on the downstream sideof the holding chamber A (not shown), so that the generated aerosolpasses through the holding chamber A on the way to the filter 7. In thefilling mode, the slider section of the valve has been pushed against aspring 8 by the action of the piston 5. This allows aerosol to flow intothe holding chamber A while a subject is able to breathe through anauxiliary chamber B that has been positioned in such a way as to be opento the air when the filling chamber A is being filled.

Methods described below can be used in association with the apparatus ofthe invention to determine the ventilating ability of a patient's lungs.Hereafter, these methods will be referred to as “Aerosol BolusDispersion” tests.

FIG. 5 shows an exemplary flow diagram for measuring the lungventilation of a patient. The volume drift control switch 201 isactivated (step 501). Pressure data is measured during respiratorycycles (step 502). The pressure data is converted to volume datafollowing placement of the mouthpiece in the mouth (step 503) and savedin data storage 109 b of computing device 109. A volume of inhalation isselected in step 504 to provide a known volume of penetration (V_(p))given the total inhalation volume. Based on the V_(p), a point in thebreathing cycle, preferably during inhalation, is determined for therelease of an aerosol bolus during (step 505). A detector 105 such as aphotocell 105 a is used to measure aerosol concentration during aplurality of respiratory cycles (step 507). The particle concentrationduring the respiratory cycle is used to calculate time constants (step508). The particle concentration is then stored and available fordisplay by the computing device 109 as a lung ventilation function (step509).

FIG. 6 is a representative flow diagram of a second method for measuringlung ventilation with the apparatus of the invention. When the volumedrift control switch 201 is activated, control of volume drift isinitiated (step 601). Pressure data is measured during inhalation andexhalation (step 602). Calculations of the volume of inhalation andexhalation are made from the pressure data saved in data storage 109 bof the computing device 109 (step 603). In particular, an analysis ofthe volume of inhalation is performed in step 604 to determine V_(p).Based on the V_(p), a time is determined for the injection of an aerosolbolus during inhalation (step 605). A light-measuring device, such asphotocell 105 a, detects the particles in the air flow during a numberof respiratory cycles. The data is then stored in the data storagesection 109 b (step 606). The stored light data is analyzed by thecomputer 109 to determine the particle concentration during inhalationof each respiratory cycle (step 607). The particle concentration duringeach inhalation determined in step 607 is then used to predict theparticle concentration (i.e., time constants) for each respectiveexhalation for a given respiratory cycle (step 608). The predictedparticle concentration is stored and available for display by thecomputing device 109 as the predicted lung ventilation (step 609). Theparticle concentration for each exhalation is also measured andcalculated for later comparison with the predicted value. Lungventilation is measured by comparing the predicted distribution of timeconstants during exhalation (i.e., predicted from the particleconcentration during inhalation) with the measured distribution of timeconstants during exhalation (step 610). The predicted and measuredparticle concentration data (i.e., time constants) is stored andavailable for display by the computing device 109 as the predicted lungventilation (step 611). The physician is then able to make diagnosisbased on any discrepancies between the predicted and measured particleconcentrations/time constants.

FIG. 7 shows an exemplary flow diagram for a method for automaticallycontrolling volume of penetration (V_(p)). When the volume drift controlswitch 201 is activated, control of volume drift is initiated (step701). Pressure data is measured during inhalation and exhalation in step702. Calculations of the volume of inhalation and exhalation are madefrom the pressure data saved in data storage 109 b (step 703). Thevolume of inhalation data is used to determine the running average valueof the volume of inhalation for a predetermined number of respiratorycycles (step 704). Based on this running average of the volume ofinhalation, the V_(p) is determined (step 705).

FIG. 8 shows another exemplary flow diagram for a method forautomatically controlling volume of penetration (V_(p)). When the volumedrift control switch 201 is activated, control of volume drift isinitiated (step 801). Pressure data is measured during inhalation andexhalation (step 802). Calculations of the volume of inhalation andexhalation are made from the pressure data saved in data storage 109 b(step 803). The volume of inhalation data is used is performed todetermine a running average value of the volume of inhalation for apredetermined number of respiratory cycles (step 804). The standard ofdeviation of the running average is calculated (step 805). The V_(p) isdetermined by setting the within a predetermined percentage of thestandard deviation of the running average value of the volume ofinhalation.

A mathematical model for the system function f is used to determine theexhaled particle concentration (C_(out)) from the saved inhalationparticle concentration data for a given breathing cycle. Because thedependence of C_(out) on the inhaled concentration C_(in) is assumedlinear, the system function is the exhaled concentration that is due toan inhaled concentration that mathematically corresponds to a delta orimpulse function.

If t is the time since the inhalation of the delta functionconcentration into the lung and Q is the rate at which air is inhaledand exhaled, then V=Qt is the volume of air inhaled up to the volume ofpenetration V_(p)=Qt_(p). For t≧t_(p), V−V_(p)=Qt−V_(p) is the amount ofair exhaled. If all the particles are exhaled (no deposition), thesystem function f(V;V_(p)) for the volume of penetration V_(p)satisfies:

∫₁ _(p) ^(∞) f(V;V _(p))dV=1.   (1)

In the general case, c_(in)(V) is not a delta function but is spread outover the volumes V where {tilde over (V)}₀≦V≦{tilde over (V)}₁. Aconsequence of this spreading is the particles inhaled at differenttimes (or V) will have different volumes of penetration. If V_(p0) isthe volume of penetration for the particles inhaled midway at

${V = \frac{\left( {{\overset{\sim}{V}}_{0} + {\overset{\sim}{V}}_{1}} \right)}{2}},$

then the volume of penetration for the other particles inhaled at V as afunction of V is

$\begin{matrix}{{{V_{p}(v)} = {V_{p\; 0} - \left\lbrack {V - \frac{\left( {{\overset{\sim}{V}}_{0} + {\overset{\sim}{V}}_{1}} \right)}{2}} \right\rbrack}};{{\overset{\sim}{V}}_{0} \leq V \leq \overset{\sim}{V}}} & (2)\end{matrix}$

The linear dependence of c_(out)(V) on c_(in)(V) in the general case cannow be expressed using the system function f(V;V_(P)(V′)) and c_(in)(V′)

{tilde over (C)} _(out)(v)=¢_({tilde over (V)}) ₀ ^({tilde over (V)}) ¹{tilde over (C)} _(in)(V′)f(V−V′;V _(p)(V′))dV′  (3)

Equation (3) models only mixing in the lung.

However, there is also mixing occurring in the pre-lung consisting ofthe machine, mouth, and larynx. This mixing occurs on inhalation as wellas exhalation. Let c_(in)(V) be the concentration of particles asmeasured by the machine for V₁≦V≦V₀. Since the flow is unidirectional,the mixing in the pre-lung is modeled as a linear and translationinvariant process relating {tilde over (C)}_(in)(V) to c_(in)(V) (Naumanand Buffham) as

{tilde over (c)} _(in)(V)=L[c _(in)(V)]=∫_(V) ₀ ^(V) ¹ c_(in)(V′)K(V−V′) dV′,   (4)

where K(V) is the system function for the mixing in the pre-lung. Tomodel K(V) accurately is difficult. Since the mixing in the pre-lung issmall compared to the mixing in the lung, it is reasonable to try tofocus on estimating the moments V_(R) and σ_(R) ² where

V _(R) =∫VK(V)dV and σ_(R) ²=∫(V−V _(R))² K(V)dV,   (5)

where V_(R) corresponds to the effective mixing volume of the pre-lungand σ_(R) ² corresponds to the variance.

The concentration c_(in)(V) measured by the machine is first processedusing equation (4) and then the resulting concentration {tilde over(c)}_(in)(V) is transformed using equation (3) to determine the particleconcentration, {tilde over (c)}_(out)(V), exiting the lung. As statedearlier, mixing also occurs in the pre-lung on exhalation. It isreasonable to use equation (4) to calculate the model prediction for theexhaled concentration c_(out)(V) from

c _(out)(V)=L[{tilde over (c)} _(out)(V)].   (6)

The model for the system function is based on the 24 generation networkmodel of the human lung devised by Weibel. The function f(V;V_(p)) isrewritten in terms of the conditional probabilities S_(i)(V;Vp) (i=1, 2,. . . , 24) and the probabilities α_(i)(V_(p)) as

$\begin{matrix}{{{f\left( {V;V_{p}} \right)} = {\sum\limits_{i = 1}^{24}{{\alpha_{i}\left( V_{p} \right)}{S_{i}\left( {V;V_{p}} \right)}}}},} & (7)\end{matrix}$

where S_(i)(V; V_(p))dV is the probability that a particle exits thelung in (V,V+dV) given that it started exhalation “near” the end ofgeneration i-1, (i=I, 2, . . . , 24) and α_(i)(V_(p)) is the fraction ofparticles that are located “near” the end of generation i-1. Near theend of generation i-1 soon will be explained. Consequently,

$\begin{matrix}{{\sum\limits_{i = 1}^{24}{\alpha_{i}\left( V_{p} \right)}} = {{1\mspace{14mu} {and}\mspace{14mu} {\int_{V_{p}}^{\infty}{{S_{i}\left( {V;V_{p}} \right)}\ {V}}}} = 1}} & (8)\end{matrix}$

Moreover, it will be shown below that the dependence of S_(i)(V; V_(p))on V_(p) is

S _(i)(V; V _(p))=S _(i)(V−V _(p)).   (9)

Using equation (9) in equation (7) allows equation (3) to be rewrittenas

$\begin{matrix}{{{\overset{\sim}{c}}_{out}(V)} = {\sum\limits_{i = 1}^{24}{\left( {\int_{{\overset{\sim}{V}}_{0}}^{{\overset{\sim}{V}}_{1}}{{{\overset{\sim}{c}}_{in}\left( V^{\prime} \right)}{\alpha_{i}\left( {V_{p}\left( V^{\prime} \right)} \right)}\ {V^{\prime}}}} \right){{S_{i}\left( {V - V_{p\; 0} + \frac{{\overset{\sim}{V}}_{0} + {\overset{\sim}{V}}_{1}}{2}} \right)}.}}}} & (10)\end{matrix}$

The construction of both α_(i)(V) and S_(i)(V−V_(p)) is based on thefollowing assumptions:

-   (1) The transit time t_(i) through each generation i-1 (i=1, 2, . .    . , 24) both on inhalation and exhalation is a random variable and    these random variables are statistically independent.-   (2) The dimensional parameters in the residence time distribution    with unit T^(δ) (T is time) are proportional to t ^(s) where t is    the expected time through generation i.

A large class of mixing in the lung will be modeled by the followingdiscrete Bernoulli distribution. It is determined by

${gt}_{i} = \frac{{gV}_{i}}{Q}$

the expected time; the time the first particle exits generation i-1; andσ²=pg² t _(i) ², the variance of the distribution. V_(i) is the volumeof generation i-1. See the Weibel Table below for values of V_(i). Inorder to study a larger class of problems, a geometric scale factor g isintroduced to demonstrably indicate that-the volume of each generationis gV_(i). The parameters are therefore t_(i), α, g, and p with α, g,and p non-dimensional constants to satisfy assumption (2). There are tworesidence times t_(i1)=αg t _(i) and

$t_{i\; 2} = {\left( {g + \frac{gp}{1 - \alpha}} \right){{\overset{\_}{t}}_{i}.}}$

To satisfy the above conditions, the probability f(t_(i)) (forgeneration i-1, i=1, 2, . . . , 24) attached to these times is

$\begin{matrix}{{f\left( t_{i} \right)} = \left\{ \begin{matrix}{{r_{1} = \frac{p}{\left( {1 - \alpha} \right)^{2} + p}},{t_{i} = t_{i\; 1}}} \\{{r_{2} = \frac{\left( {1 - \alpha} \right)^{2}}{\left( {1 - \alpha} \right)^{2} + p}},{t_{i} - {t_{i\; 1}.}}}\end{matrix} \right.} & (11)\end{matrix}$

Assuming that all particles enter the lung at the same time, the problemis to determine the distribution of particles in each generation of thelung after the additional amount of air V_(p) is inhaled using thedistribution given by equation (11). It is useful to change variablefrom the time t since the start of inhalation, to V=Qt, the volume ofair inhaled. It is also useful to calculate the cumulative distributionthat gives the fraction of particles that already exited each generationas a function of air inhaled V. It is then an easy calculation todetermine the percentage of particles in each generation at the end ofinhalation.

For example, let I₁(V) be the fraction of particles that have exitedgeneration zero as a function of air inhaled V≧0 . Then, using equation(9) with i=1 gives

$\begin{matrix}{{I_{1}(V)} = \left\{ \begin{matrix}{0,} & {0 \leq V \leq V_{11}^{T}} \\r_{1} & {V_{11}^{T} \leq V < V_{12}^{T}} \\{1,} & {V_{12}^{T} < V}\end{matrix} \right.} & (12)\end{matrix}$

The important points in the domain of I₁(V) are V₁₁ ^(T)=αgV₁=Qt₁₁ and

${V_{12}^{T} = {{\left( {g + \frac{gp}{1 - \alpha}} \right)V_{1}} = {{Qt}_{12} \cdot {gV}_{1}}}};$

is the volume of generation zero.

To calculate I₂(V), the fraction of particles that have exitedgeneration one as a function of V, use the assumption that the randomvariables t₁ and t₂ are independent. Initially, there are four criticalvalues in the domain:

V₂₁^(T) = α g(V₁ + V₂) = Q(t₁₁ + t₂₁)${V_{11} + V_{12}} = {{\alpha \; {gV}_{1}} + {\left( {g + \frac{gp}{1 - \alpha}} \right)V_{2}}}$${V_{21} + V_{22}} = {{\alpha \; {gV}_{2}} + {\left( {g + \frac{gp}{1 - \alpha}} \right)V_{1}}}$$V_{22}^{T} = {{\left( {g + \frac{gp}{1 - \alpha}} \right)\left( {V_{1} + V_{2}} \right)} = {Q\left( {t_{12} + t_{22}} \right)}}$

The definition of Ĩ₂ (the tilde to be explained) is

${{\overset{\sim}{I}}_{2}(V)} = \left\{ \begin{matrix}{0,} & {0 \leq V < V_{21}^{T}} \\{r_{1}^{2},} & {V_{21}^{T} \leq V < {V_{11} + V_{22}}} \\{{r_{1}^{2} + {r_{1}r_{2}}},} & {{V_{11} + V_{22}} \leq {V_{21} + V_{12}}} \\{{r_{1}^{2} + {2r_{1}r_{2}}},} & {{V_{21} + V_{12}} \leq V < V_{22}^{T}} \\{1,} & {V_{22}^{T} \leq {V.}}\end{matrix} \right.$

Observe that the average value of V₁₁+V₂₂ and V₂₁+V₁₂ in the domain ofĨ₂ is midway between V₂₁ ^(T) and V₂₂ ^(T). A reasonable simplificationis to attach the probability r_(i) ²+2r₁r₂ to this midpoint and thusgroup together the two similar paths the corresponding particles in thelung have traveled. This resulting function is written I₂(V) and givenas

$\begin{matrix}{{I_{2}(V)} = \left\{ \begin{matrix}{0,} & {0 \leq V < V_{21}^{T}} \\{r_{1}^{2},} & {V_{21}^{T} \leq V < {V_{21}^{T} + \frac{V_{22}^{T} - V_{21}^{T}}{2}}} \\{{r_{1}^{2} + {r_{1}r_{2}}},} & {{V_{21}^{T} + \frac{V_{22}^{T} - V_{21}^{T}}{2}} \leq V < V_{22}^{T}} \\{1,} & {V_{22}^{T} \leq V}\end{matrix} \right.} & (13)\end{matrix}$

The function I_(i)(V) (i=1, 2, . . . , 24) is the fraction of particlesthat have exited generation i-1 as a function of V and is calculatedusing independence of random variables t_(i), the distribution inequation (11), and as done in the definition of I₂, grouping togetherall paths that have probability r₁ ^(i-k)r₂ ^(k) for k=0, 1, . . . , i.It can be shown that the average value of V where these particles exitgeneration i-1 is

$V_{i\; 1}^{T} + \frac{k\; \Delta \; V_{i}}{i}$

where

V_(i)^(T) = V₁ + V₂ + ⋯ + V_(i) V_(i 1)^(T) = α g$V_{i\; 2}^{T} = {\left( {g + \frac{gp}{1 - \alpha}} \right)V_{i}^{T}}$Δ V_(i) = V_(i 2)^(T) − V_(i 1)^(T)

There are

$\frac{i!}{{k!}{\left( {i - k} \right)!}}$

such paths with probability r₁ ^(i-k)r₂ ^(k). Thus, the definition ofI_(i) is

${I_{i}(V)} = \left\{ \begin{matrix}{0,} & {0 \leq V < V_{i\; 1}^{T}} \\{r_{1}^{i},} & {V_{i\; 1}^{T} \leq V < {V_{i\; 1}^{T} + \frac{\Delta \; V_{i}}{i}}} \\{{r_{1}^{i} + {\frac{i!}{{1!}{\left( {i - 1} \right)!}}r_{1}^{i - 1}r_{2}}},} & {{V_{i\; 1}^{T} + \frac{\Delta \; V_{i}}{i}} \leq V < {V_{i\; 1}^{T} + \frac{2\Delta \; V_{i}}{i}}} \\\cdots & \; \\{{\sum\limits_{j = 0}^{k}{\frac{i!}{{j!}{\left( {i - j} \right)!}}r_{1}^{i - j}r_{2}^{j}}},} & {{V_{i\; 1}^{T} + \frac{k\; \Delta \; V_{i}}{i}} \leq V < {V_{i\; 1}^{T} + \frac{\left( {k + 1} \right)\Delta \; V_{i}}{i}}} \\\cdots & \; \\{1,} & {V_{i\; 2}^{T} \leq V}\end{matrix} \right.$

The grouping together of paths reduced the number of jumps in I_(i)(V)from 2^(i) to i+1, a considerable savings in accounting with anacceptable loss in accuracy. Finally, I₀(V) is defined to be 1 for allV≧0 and corresponds to all particles entering the system immediately.Putting V=V_(p0) will emphasize that I_(i)(V_(p0)) corresponds to thedistribution of particles at the end of inhalation.

Fortunately, it is possible to further simplify the expression forI_(i)(V_(p0)) using

$\begin{matrix}{I_{i} \approx {\sum\limits_{j = 0}^{k}{\frac{i!}{{k!}{\left( {i - k} \right)!}}r_{1}^{i - k}r_{2}^{k}}} \approx {\frac{1}{\sqrt{2\; \pi \; {ir}_{1}r_{2}}}{\int_{- \infty}^{k}{^{{{- {({x - {ir}_{2}})}^{2}}/2}{ir}_{1}r_{2}}\ {x}}}}} & (14)\end{matrix}$

In order to change to the continuous variable V_(p0) in equation (14)from the integer variable k use the equations

${V_{p}(x)} = {V_{i\; 1}^{T} + \frac{x\; \Delta \; V}{i}}$

and V_(p)(k)=V_(p0):

${I_{i}\left( V_{p\; 0} \right)} = {\frac{1}{\sqrt{2\; \pi \; \sigma_{i}^{2}}}{\int_{- \infty}^{V_{p\; 0}}{^{{{- {({x - V_{i\; 1}^{T} - {r_{2}\Delta \; V_{i}}})}^{2}}/2}\sigma_{i}^{2}}\ {x}}}}$

where

$\sigma_{i}^{2} = {\frac{r_{1}{r_{2}\left( {\Delta \; V_{i}} \right)}^{2}}{i}.}$

Letting

$y = \frac{x}{{gV}_{i}^{T}}$

and replacing r₁, r₂, and ΔV_(i) with their equivalent in terms of a, g,p, and V_(i) ^(T) gives

$\begin{matrix}{{{I_{i}\left( {\frac{V_{p\; 0}}{g};p} \right)} = {{I_{i}\left( V_{p\; 0} \right)} = {\frac{1}{\sqrt{\frac{2\; \pi \; p}{i}}}{\int_{- \infty}^{V_{p\; 0}/{gV}_{i}^{T}}{^{{- {({y - 1})}^{2}}/\frac{2\; p}{i}}\ {y}}}}}},{i = 1},2,\; \cdots \;,24} & (15)\end{matrix}$

The notation for I_(i) has changed to show the dependence on theparameters g and p in addition to V_(p0). Note that, with theapproximation given by equation (14), the dependence on a is gone. Thedefinition of I₀(V_(p)) remains unchanged.

Since I_(i) gives the fraction of particles that have exited generationi-I (i-1=1, 2, . . . , 23), the fraction of particles in generation i-Iat the end of inhalation is q_(i)=I_(i-1)−I_(i). The fraction ofparticles beyond generation 23 is given by q₂₅=I₂₄.

To calculate how the particles exit the lung, first assume that all theparticles in the deeper half of generation i-I and shallower half ofgeneration i are all located at the end of generation i-1. This is thedefinition of α_(i) for i=1, 2, . . . , 23. α₂₄ includes all theparticles in the deeper half of generation 23 and beyond. This accountsfor all the particles in the lung except for the particles in theshallower half of generation zero, which should be negligible for theuseful values of V_(p0). The explicit formulas are (i.e., lettingx=y−1/√{square root over (p/i)} in equation (15))

${\alpha_{1}\left( {\frac{V_{p\; 0}}{g},p} \right)} = {\frac{1}{2\sqrt{2\; \pi}}{\int_{{({\frac{V_{p\; 0}}{{gV}_{2}^{T}} - 1})}/\sqrt{\frac{p}{2}}}^{\infty}{^{{- x^{2}}/2}\ {x}}}}$${\alpha_{i}\left( {\frac{V_{p\; 0}}{g},p} \right)} = {\frac{1}{2\sqrt{2\; \pi}}{\int_{{({\frac{V_{p\; 0}}{{gV}_{i + 1}^{T}} - 1})}/\sqrt{\frac{p}{i + 1}}}^{{({\frac{V_{p\; 0}}{{gV}_{i - 1}^{T}} - 1})}/\sqrt{\frac{p}{i - 1}}}{^{{- x^{2}}/2}{x}}}}$i = 2, 3, ⋯ , 23${\alpha_{24}\left( {\frac{V_{p\; 0}}{g},p} \right)} = {\frac{1}{2\sqrt{2\; \pi}}{\int_{- \infty}^{{({\frac{V_{p\; 0}}{{gV}_{23}^{T}} - 1})}/\sqrt{\frac{p}{23}}}{^{{- x^{2}}/2}\ {x}}}}$

The construction of the conditional probabilities S_(i)(V;V_(p)) issimilar to α_(i)(V). This yields

$\begin{matrix}{{S_{i}\left( {V;V_{p}} \right)} = {{S_{i}\left( {{V - V_{p}},g^{e},p^{e}} \right)} = {\frac{1}{g^{e}V_{i}^{T\sqrt{\frac{2\pi \; {ip}^{e}}{{({i + 1})}^{2}}}}}^{{- {({\frac{V - V_{p}}{g^{e}V_{i}^{T}} - 1})}^{2}}/\frac{2{ip}^{e}}{{({i + 1})}^{2}}}}}} & (17)\end{matrix}$

Note that the dependence of S_(i) on V and V_(p) and is in the formV−V_(p). The meanings of g^(e) and p^(e) are the same as used oninhalation. The value of g^(e) is the geometric scale factor for thevolume of the lung on exhalation and p^(e) is the variance factor. Thecorresponding factors on inhalation will now be written as g^(i) andp^(i).

The first and second moments of the random variable y_(i) withdistribution S_(i)(y,g³,p^(e)) will be important for theoretical reasonsand for estimating parameters from experimental data. These moments are

$\begin{matrix}{{E\left( y_{i} \right)} = {{g^{e}V_{i}^{T}\mspace{14mu} {and}\mspace{14mu} {E\left( y_{i}^{2} \right)}} = {\left( {g^{e}V_{i}^{T}} \right)^{2}\left( {1 + \frac{{ip}^{e}}{\left( {i + 1} \right)^{2}}} \right)}}} & (18)\end{matrix}$

The system function for mixing in the lung can now be written as (seeequation (7))

${f\left( {{v;V_{p}},g^{i},p^{i},g^{e},p^{e}} \right)} = {\sum\limits_{i = 1}^{24}{{\alpha_{i}\left( {\frac{V_{p}}{g^{i}},p^{i}} \right)}{S_{i}\left( {{V - V_{p}},g^{e},p^{e}} \right)}}}$

It can be demonstrated through simulation of f for the reasonable rangeof parameter values that for a factor r of order 1

f(V;V _(p) ,rg ^(i) ,p ^(i) ,rg ^(e) ,p ^(e))=f(V;V _(p) ,g ^(i) ,p ^(i),g ^(e) ,p ^(e))

Letting r=(g^(i))³¹ ¹

$\begin{matrix}{{f\left( {{V;V_{p}},1,p^{i},\frac{g^{e}}{g^{i}},p^{e}} \right)} = {f\left( {{V;V_{p}},g^{i},p^{i},g^{e},p^{e}} \right)}} & (19)\end{matrix}$

The model shows that the exhaled concentration from the lung containsinformation only on the relative effective volume g³/g^(j) in additionto p^(i) and p^(e).

In view of the mixing in the prelung with volume V_(R) (see equation(5)), equation (2) becomes

$\begin{matrix}{{V_{p}(V)} = {V_{p\; 0} - \left( {V - \left( {\frac{V_{0} + V_{1}}{2} + V_{R}} \right)} \right)}} & (20)\end{matrix}$

with

$\frac{{\overset{\sim}{V}}_{0} + {\overset{\sim}{V}}_{1}}{2} = {\frac{V_{0} + V_{R} + V_{1} + V_{R}}{2}.}$

Consequently, equation (10) becomes

$\begin{matrix}{{{\overset{\sim}{c}}_{out}\left( {V,\frac{g^{e}}{g^{i}},p^{i},{p^{e};V_{p\; 0}}} \right)} = {\sum\limits_{i = 1}^{24}\; {\int_{{\overset{\sim}{V}}_{0}}^{{\overset{\sim}{V}}_{1}}{{{\overset{\sim}{c}}_{in}\left( V^{\prime} \right)}{\alpha_{i}\left( {{V_{p}\left( V^{\prime} \right)},p^{i}} \right)}{S_{i}\left( {{V - \left( {V_{p\; 0} + \frac{V_{0} + V_{1}}{2} + V_{R}} \right)},\frac{g^{e}}{g^{i}},p^{e}} \right)}\ {{V^{\prime}}.}}}}} & (21)\end{matrix}$

Using equation (21) in equation (6) gives the model prediction for theexhaled particle concentration measured by the apparatus as

$\begin{matrix}{{c_{out}\left( {V,\frac{g^{e}}{g^{i}},p^{i},{p^{e};V_{p\; 0}}} \right)} = {\int{{{\overset{\sim}{c}}_{out}\left( {\overset{\sim}{V},\frac{g^{e}}{g^{i}},p^{i},{p^{e};V_{p\; 0}}} \right)}{K\left( {V - \overset{\sim}{V}} \right)}{{\overset{\sim}{V}}.}}}} & (22)\end{matrix}$

The integration in equation (22) is over the interval where {tilde over(c)}_(out) is nonzero.

It is clear from equation (22) that the parameters to be estimatedinclude

$\frac{g^{e}}{g^{i}},$

p^(i), and p^(e). V_(po) is the average volume of penetration into thelung, whereas V_(po)+V_(R) is the total volume of air measured by theapparatus at the end of inhalation. Thus V_(po) will be known once V_(R)is known or estimated.

Let c_(out) ^(M)(V_(i)) denote the actual exhaled concentration measuredby the apparatus at the discrete values V_(i), i=1 , 2, . . . , n. Dueto measurement noise, inadequacy of the model, etc, the relationshipbetween the measured output and the model prediction is

c _(out) ^(M)(V _(i))=c _(out)(V _(i), . . . )   (23)

At this stage, it is reasonable to use the minimum least squarescriterion to estimate the parameters

Minimize:

$\begin{matrix}{{F\left( {\frac{g^{e}}{g^{i}},p^{i},{p^{e};V_{p\; 0}}} \right)} = {\sum\limits_{i = 1}^{n}\; {\left( {{c_{out}^{M}\left( V_{i} \right)} - {c_{out}\left( {V_{i},\frac{g^{e}}{g^{i}},p^{i},{p^{e};V_{p\; 0}}} \right)}} \right)^{2}.}}} & (24)\end{matrix}$

It is useful to calculate the first two moments of the model predictionc_(out)(V, . . . )

E(V)=∫Vc _(out)(V, . . . )dV/∫c _(out)(V, . . . )dV

E(V−E(V))²=∫(v−E(V))² c _(out)(V, . . . )dV/∫c _(out)(V, . . . )dV

A direct calculation of E(V) using equation (22) gives

$\begin{matrix}{{E(V)} = {V_{p\; 0} + {2\; V_{R}} + \frac{V_{0} + V_{1}}{2} + {\frac{g^{e}}{g^{i}}{A_{0}\left( p^{i} \right)}V_{p\; 0}}}} & (25)\end{matrix}$

Recall that the variable V is related to the volume of air through themachine with

$\frac{V_{0} + V_{1}}{2}$

(the center of the c_(in)(V) distribution) playing the role of theorigin. In arriving at 2 equation (25), the following approximation wasused:

${\sum\limits_{i = 1}^{24}\; {{\alpha_{i}\left( {V_{p},p^{i}} \right)}V_{i}^{T}}} \approx {{A_{0}\left( p^{i} \right)}V_{p}} \approx {\left( {1.00919 + {0.0688435\; p^{i}}} \right)V_{p}}$

The important term in equation (25) is

$\frac{g^{e}}{g^{i}}{A_{0}\left( p^{i} \right)}{V_{p\; 0}.}$

It is approximately V_(p0) corresponding to the additional volume withinwhich the typical particle exits the lung given that the volume ofpenetration into the lung is V_(p0). The model shows that this value isinflated by the intrinsic mixing occurring during inhalation (quantifiedby the parameter p^(i)) and the relative effective volume of the lung

$\frac{g^{e}}{g^{i}}.$

The direct calculation of E(V−E(V))² gives

$\begin{matrix}{{{E\left( {V - {E(V)}} \right)}^{2} = {\sigma_{R}^{2} + {\left( \frac{g^{e}}{g^{i}} \right)^{2}\left( {{B_{0}\left( p^{i} \right)} + {p^{e}{B_{1}\left( p^{i} \right)}}} \right)\left( {\sigma_{R}^{2} + V_{p\; 0}^{2} + \sigma_{in}^{2}} \right)} - {\left( \frac{g^{e}}{g^{i}} \right)^{2}\left( {{A_{0}\left( p^{i} \right)}V_{p\; 0}} \right)^{2}}}};} & (26)\end{matrix}$

where σ_(R) ² is defined by equation (5) and σ_(in) ² is the variance ofthe C_(in)(V) distribution.

The functions B_(o)(p^(i)) and B₁(p^(i)) have derivations similar toA₀(p^(i)):

${{\sum\limits_{i = 1}^{24}\; {{\alpha_{i}\left( {V_{p},p^{i}} \right)}\left( V_{i}^{T} \right)^{2}}} \approx {{B_{0}\left( p^{i} \right)}V_{p}^{2}}};$and${\sum\limits_{i = 1}^{24}\; {{\alpha_{i}\left( {V_{p},p^{i}} \right)}\frac{\left( V_{i}^{T} \right)^{2}i}{\left( {i + 1} \right)^{2}}}} \approx {{B_{1}\left( p^{i} \right)}{V_{p}^{2}.}}$

The sample mean V and variance (V−{overscore (V)})² are defined to be

${\overset{\_}{V} = {\sum\limits_{i - 1}^{n}\; {V_{i}{{c_{out}^{M}\left( V_{i} \right)}/{\sum\limits_{i = 1}^{n}{c_{out}^{M}\left( V_{i} \right)}}}}}};$and$\overset{\_}{\left( {V - \overset{\_}{V}} \right)^{2}} = {\sum\limits_{i = 1}^{n}{\left( {V_{i} - \overset{\_}{V}} \right)^{2}{{c_{out}^{M}\left( V^{i} \right)}/{\sum\limits_{i = 1}^{n}{{c_{out}^{M}\left( V^{i} \right)}.}}}}}$

Therefore, in order to have initial estimates for

$\frac{g^{e}}{g^{i}},$

p^(i), and p^(e), use the approximations E(V)≈ V and E(V−E(V))²≠(V−{overscore (V)})² in equations (25) and (26), and solve for

${\frac{g^{e}}{g^{i}}p^{i}} = {p^{e} = p}$

(assume p^(i)=p^(e) for simplicity). Use these as starting values in thenumerical procedures for minimizing

$F\left( {\frac{g^{e}}{g^{i}},p^{i},{p^{e};V_{p\; 0}}} \right)$

defined in equation (24).

As a non-limiting example of the method of the present invention, theexhaled aerosol concentration as a function of volume exhaled can beanalyzed by determining the volume difference at half the peakconcentration, as shown in FIG. 9. In this method, the volume exhaled isdivided by the volume of penetration. At the volume at which half thepeak concentration is reached and on the increasing slope side of theexhaled concentration profile, the initial volume value V₁ is obtainedcorresponding to the volume coordinate of that point. On the decliningconcentration side of the exhaled concentration profile the final volumevalue V₂ is obtained corresponding to the volume coordinate of theconcentration point at which the concentration is half the maximum. Theresultant measure of dispersion is therefore V₂−V₁. Since each volumevalue is divided by the volume of penetration, the expected result ofV₂−V₁ should be approximately the same for all volumes of penetration aslong as the bolus does not penetrate into the gas exchange region of thelung. Should the result of V₂−V₁ change in a statistically significantway when compared to previous differentials for smaller volumes ofpenetration, the volume of penetration at which that occurs will bedeemed the appropriate volume for introduction of a therapeutic aerosol.The output of the apparatus is the concentration of aerosol c_(out) as afunction of volume exhaled V. These two variables can be related bythree parameters as:

c _(out)(V, p ^(i), g, p^(e))=∫_(-∞) ^(∞) {tilde over (c)} _(out)({tildeover (V)}, p ^(i), g, p^(e))K(V−{tilde over (V)})d{tilde over (V)}  (27)

where the three parameters are:

-   -   p^(i), p^(e)=intrinsic mixing on inhalation and exhalation,        respectively; and    -   g=relative effective volume (i.e., the effective volume of lung        on exhalation g^(e) divided by effective volume of lung on        inhalation g^(i)).

These three parameters are determined by comparing the output from theabove Equation (27) to the actual data for various values of theparameters. This is done at a given volume of penetration V_(p0).

Equation (27) is derived by the following method:

-   -   a. c_(out)(V, p^(i), g, p^(e)) is compared to the actual data        from the apparatus;    -   b. c_(in)(V)=concentration of particles as a function of total        volume measured by the apparatus upon inhalation, where        (V_(l)≦V≦V_(r)); and    -   c. {tilde over (c)}_(in)(V)=∫_(V) _(l) ^(V) ^(r) c_(in)({tilde        over (V)})K(V−{tilde over (V)})d{tilde over (V)}, where K is to        be determined.

One possibility for determining K is the expression:

${{K(V)} = {\frac{1}{\sqrt{2{\pi\sigma}_{R}}}^{- \frac{{({V - V_{R}})}^{2}}{2\sigma_{R}^{2}}}}},$

where V_(R) is the effective volume of the prelung, and σ_(R) is thestandard deviation of mixing in the prelung.

In addition, c_(out) is approximately:

${{\overset{\sim}{c}}_{out}\left( {V,p^{i},g,p^{e}} \right)} = {\sum\limits_{i = 1}^{24}\; {\left( {\int_{- \infty}^{\infty}{{{\overset{\sim}{c}}_{in}\left( V^{\prime} \right)}{\alpha_{i}\left( {{V_{p}\left( V^{\prime} \right)},p^{i}} \right)}\ {V^{\prime}}}} \right){S_{i}\left( {{V - \left( {V_{p\; 0} + V_{R} + \frac{V_{l} + V_{r}}{2}} \right)},g,p^{e}} \right)}}}$

where:

${{V_{p}\left( V^{\prime} \right)} = {V_{p\; 0} + V_{R} + \frac{V_{l} + V_{r}}{2} - V^{\prime}}};$${V_{p\; 0} = {{volume}\mspace{14mu} {of}\mspace{14mu} {penetration}\mspace{14mu} {for}\mspace{14mu} {particles}\mspace{14mu} {at}\mspace{14mu} \frac{V_{l} + V_{r}}{2}}};$

V_(i)=volumes from Weibel's table (see below) i=1, 2, . . . , 24, V_(i∞)^(Γ)=V₁+V₂− . . . +V_(i);

${{\alpha_{1}\left( {t,p^{i}} \right)} = {\frac{1}{2\sqrt{2\pi}}{\int_{{({\frac{t}{V_{2\infty}^{T}} - 1})}/\sqrt{\frac{p^{i}}{2}}}^{\infty}{^{{- x^{2}}/2}\ {x}}}}},{{{{at}\mspace{14mu} i} = 1};}$${{\alpha_{i}\left( {t,p^{i}} \right)} = {\frac{1}{2\sqrt{2\pi}}{\int_{{({\frac{t}{V_{2\infty}^{T}} - 1})}/\sqrt{\frac{p^{i}}{i + 1}}}^{{({\frac{t}{V_{i - {1\infty}}^{T}} - 1})}/\sqrt{\frac{p^{i}}{i - 1}}}{^{{- x^{2}}/2}\ {x}}}}},{i = 2},3,\ldots \mspace{14mu},{23;}$${{\alpha_{24}\left( {t,p^{i}} \right)} = {\frac{1}{2\sqrt{2\pi}}{\int_{- \infty}^{{({\frac{t}{V_{23\infty}^{T}} - 1})}/\sqrt{\frac{p^{i}}{23}}}{^{{- x^{2}}/2}\ {x}}}}},{{{{at}\mspace{14mu} i} = 24};}$and${S_{i}\left( {{y;g},p^{e}} \right)} = {\frac{1}{{gV}_{i\; \infty}^{T}\sqrt{\frac{2\pi \; {ip}^{e}}{\left( {i + 1} \right)^{2}}}}{^{{- {({\frac{y}{{gV}_{i\; \infty}^{T}} - 1})}^{2}}/\frac{2\; {ip}^{e}}{{({i + 1})}^{2}}}.}}$

Moreover, Weibel's Table discussed above is given by:

 V(1) = 30.5  V(2) = 11.25  V(3) = 3.97  V(4) = 1.52  V(5) = 3.46  V(6)= 3.3  V(7) = 3.53  V(8) = 3.85  V(9) = 4.45 V(10) = 5.17 V(11) = 6.21V(12) = 7.56 V(13) = 9.82 V(14) = 12.45 V(15) = 16.4 V(16) = 21.7 V(17)= 29.7 V(18) = 41.8 V(19) = 61.1 V(20) = 93.2 V(21) = 139.5 V(22) =224.3 V(23) = 350.0 V(24) = 591.0

While the above derivations were performed for an aerosol concentrationas a function of time at a constant flow rate, it should be noted thatboth time and volume are interchangeable. Thus, volume and dimensionlessvolume (i.e., the volume of inhalation divided by the average volumeinhaled), could be used in place of time in the above derivation. Toillustrate this concept, a time domain derivation of another element ofthe invention is presented below.

When analyzing the response curves obtained for subjects inhalingaerosol boluses, background art methods did not account for thenon-symmetry of the response curves in their mathematical treatments.This non-homogeneity of ventilation is not only associated with diseasedsubjects but also with healthy subjects as well. Therefore, mathematicalmodels for the present method of the present invention were designed totreat mixing in both diseased and healthy subjects and typically includea term for the non-homogeneity of ventilation.

The above observations provide for a model formulation beginning with ahypothetical mixing chamber in which the extent of mixing could bevaried. Models of background art methods have used the simplifyingassumption of a Guassian shape for the response curves exhalationprofile. However, the present invention considers the response curves tobe non-Guassian (i.e., asymmetric). The appearance of thesenon-symmetric response curves is strikingly similar to a Gammadistribution. Such a distribution is commonly used to model mixing instirred reaction vessels. A system of such reaction vessels, whenmodeled appropriately, results in the following expression for the exitconcentration:

$\begin{matrix}{{E(t)} = {\frac{p^{p}}{t^{p}{\Gamma (p)}}t^{p - 1}^{\frac{- {pt}}{\overset{\sim}{t}}}}} & (28)\end{matrix}$

-   where: t=the exit age of a particle flowing through the system;    -   t=the mean residence time of the particles in the system;    -   E(t)=the outlet concentration for a given unit impulse of a        pulsed tracer; and    -   Γ=the gamma function=Γ(p)=(p−1)!

Equation (28) is generally referred to as the “tanks-in-series model,”in which p is the number of reactors in series. When p=1, thedistribution is exponential and is the standard distribution expectedfor a single stirred-tank reactor. As p approaches infinity, the exittime for all the particles becomes the same, thus approaching aplug-flow condition. For this extreme, the response becomes increasinglysteeper and approaches a normal distribution. This enables a comparisonof the “tanks-in-series” model with other background art dispersionmodels. Such a comparison yields an important dimensionless measure, thePeclet number N_(Pe)), which is used to relate the contribution of theconvective mixing over the mixing by dispersion. For large p, N_(Pe)=2pand for small p, N_(Pe)=2(p−1).

Another important feature of the Gamma Distribution model of Equation(28) is the potential to add a by-pass loop which accounts for thatfraction of the aerosol bolus not penetrating the alveolar ducts. Inaddition, another term can be introduced that models the effect ofincreased regional time constants due to obstruction. This assumes thatthe upper airways contribute little to the overall ventilation in thelung. Therefore, any aerosol remaining in the upper airways basicallyby-passes the ventilation section (i.e., lower airways and alveoli) ofthe lung. This accounts for the parallel ventilation. A gammadistribution with a by-pass loop is given in Equation (28) as:

$\begin{matrix}{{E(t)}_{\Gamma} = {\frac{\left( {p\; \beta} \right)^{p}}{t^{p}{\Gamma (p)}}t^{({p - 1})}^{\frac{{- p}\; \beta \; t}{\overset{\sim}{t}}}}} & (29)\end{matrix}$

-   where: β=by-pass loop parameter; p1 t=the exit age of a particle    flowing through the system;    -   t=the mean residence time of the particles in the system;    -   E(t)_(Γ)=the outlet concentration for a given unit impulse of a        pulsed tracer with a by-pass loop; and    -   Γ=the gamma function=Γ(p)=(p−1)!.

Variable opening volumes for different lung regions, due either tovariable stresses in an erect subject or to differing products ofresistance and capacitance in the pathways, lead to alveoli opening andfilling at different times during the inhalation. Since the regionaltime constants increase with obstruction, less aerosol can penetrate theobstructed airways to the alveoli. Thus, on exhalation this aerosolemerges unmixed by the action of the alveoli. In addition, the aerosolis also coming from regions with greater time constants that exit moreslowly and over a longer period than normal.

The parameter describing the fraction of flow that enters the mixingchamber is defined as letting:

-   -   β=Q₁/Q_(T) the fraction of flow entering the mixing section; and    -   t=V/Q_(T) but, t _(p)=V/Q₁=V/βQ_(T)= t/β

-   where: t=mean residence time of the entire system;    -   t _(p)=mean residence time of the mixing section;    -   V=volume of the entire system;    -   Q_(T)=total flow through the system;    -   Q₁=flow through the mixing section; and    -   Q₂=flow by-passing the mixing section.

Therefore, the mixing in the stirred reactors can be described by:

$\begin{matrix}{{E(t)}_{\Gamma} = {\frac{(p)^{p}}{t^{p}{\Gamma (P)}}t^{({p - 1})}{^{\frac{- {pt}}{{\overset{\sim}{t}}_{p}}}.}}} & (30)\end{matrix}$

However, since t _(p)= t _(p)/β, Equation (30) can be rewritten as:

$\begin{matrix}{{E(t)}_{\Gamma} = {\frac{\left( {p\; \beta} \right)^{p}}{{\overset{\_}{t}}^{p}{\Gamma (p)}}t^{({p - 1})}{^{\frac{{- p}\; \beta \; t}{\overset{\sim}{t}}}.}}} & (31)\end{matrix}$

Equation (30) is the exit-age distribution of the mixing section whenthere is by-passing. Defining the reduced time as θ=t/ t, and notingthat E(θ)_(1′)= t E(t)_(Γ), the exit age distribution of the Γ-mixingsection for a unit impulse is given in terms of reduced time θ by:

$\begin{matrix}{{E(\theta)}_{\Gamma} = {\frac{\left( {p\; \beta} \right)^{p}}{\Gamma (p)}\theta^{({p - 1})}^{{- p}\; {\beta\theta}}}} & (32)\end{matrix}$

Taking the Laplace transform of Equation (31) gives the transferfunction for the mixing section alone as:

$\begin{matrix}{{E(s)} = {\frac{C_{1}(s)}{C_{0}(2)} = {\left\lbrack \frac{p\; \beta}{s + {p\; \beta}} \right\rbrack^{p}.}}} & (33)\end{matrix}$

Performing a material balance at the point where the by-pass stream andthe mixing section stream join to form the outlet stream we have:

C ₂ Q _(t) =Q ₁ C ₁ +Q ₂ C _(o).   (34)

Dividing Equation (34) throughout by Q_(t) and rearranging bysubstituting for β yields

C ₂ Q _(t) =C ₁β+(1−β)C _(o)   (35)

Taking the Laplace transform of Equation (35) and dividing throughout byC_(o)(s) yields:

$\begin{matrix}{{E(s)} = {\frac{C_{2}(s)}{C_{0}(2)} = {{\frac{C_{2}(s)}{C_{0}(2)}\beta} + {\left( {1 - \beta} \right).}}}} & (36)\end{matrix}$

Upon substituting Equation (32) in the above equation, the result forthe output of the composite is:

$\begin{matrix}{{H(s)} = {\frac{C_{2}(s)}{C_{0}(2)} = {{\left\lbrack \frac{p\; \beta}{s + {p\; \beta}} \right\rbrack \beta} + {\left( {1 - \beta} \right).}}}} & (37)\end{matrix}$

Now, assuming a delta function type input signal for C_(o)(s), theinverse transform of the function shown in Equation (34) then gives thecomplete system definition for the output concentration C₂(θ) in thetime domain from the model predicted for an impulse-type input signal,where, δ(θ)=the dirac delta function and C₂(θ) is given by:

$\begin{matrix}{{C_{2}(\theta)} = {{\left\lbrack \frac{{\beta \left( {p\; \beta} \right)}^{p}}{\Gamma (p)} \right\rbrack \theta^{({p - 1})}^{{- p}\; {\beta\theta}}} + {\left( {1 - \beta} \right){{\delta (\theta)}.}}}} & (38)\end{matrix}$

The first term in Equation (38) describes the mixing of the impulse-typeinput signal occurring for the amount of air flow entering the mixingchamber accounted for by β. The second term is purely a by-pass termrelating to the amount of air by-passing the mixing chamber. Theby-passed air is instantly detected at the time when the input impulseis given.

The model parameters p and β can be easily determined from the datacollected by the method of moments. However, when the method was used tocalculate p and β for an ideal impulse, the method failed to estimatecorrect values of p and P. Therefore, the present invention performsthis parameter estimation function by a curve-fitting technique with thegoodness-of-fit measured by minimizing the sum of the differencessquared.

The ventilation parameter, p, has a minimum value of 1 for complete(i.e. uniform) mixing. If there is no by-passing (β=1) and for thespecial case where p=1, then Equation (37) reduces to the exponentialdistribution. An increasing value of p is used to model the effect ofincreased ventilation or reduced homogeneous mixing. As p approachesinfinity, no mixing occurs and the output distribution becomes identicalto the input distribution. This is the case of perfect ventilation.Increasing values of p also cause the peak-concentration time to occurlater, approaching θ=1/β as an upper limit. Since p is actually thenumber of reactors in series, the result of increasing the number ofreaction vessels in series is to decrease the completeness of the mixingfor a given volume of the system.

The fraction of flow which enters the mixing section (determined by β,the by-pass parameter) is used as a measure of the non-homogeneity ofventilation. The underlying assumption is that the fraction of flowwhich does not enter the ventilation section undergoes no ventilation.That is, based on the assumption that the upper airways contributerelatively little to the ventilation between tidal and residual air,only the fraction of the aerosol which penetrates past the upper airwaysis assumed to undergo ventilation. As the regional time constantsincrease, owing to airway obstruction, additional alveoli are recruitedalong less obstructed pathways. This causes the aerosol in the inhaledbolus to traverse additional airways and more of the air flow stream toby-pass the ventilation section. In other words, a larger fraction ofthe aerosol remains in the airways rather than penetrating theairspaces. An analogous situation occurs when the depth to which thebolus is inhaled in a healthy subject is decreased. The decreasedpenetration causes a decrease in the fraction of aerosol penetrating tothe airspaces and a decreased value of β is observed. A decreasing βcauses the peak concentration to occur at a later time, where θ=1 as thelower limit. If an increase in mixing occurs, as should be the case fordecreased penetration, the peak concentration may be offset, resultingin negligible net movement of the peak.

Therefore, in individuals with airway obstruction or restriction; (1)when the aerosol passes an obstructed airway the value of p or β willchange; and (2) the volume at which the change in p or β occurs is thesite of the obstruction and the volume at which the therapeutic aerosolshould be injected. In healthy subjects, the values of p and β should beseen to fluctuate relatively little at any inhaled volume of aerosolbolus, as long as the aerosol is not inhaled into the gas exchangeregion of the lung and as long as Equation (37) is solved for thedimensionless volume.

Further, as a non-limiting example of the methods discussed above, thediagnosis of asthma may be done using the content of multiple breathswhen a bolus is inhaled on the first breath only. If the bolus ofaerosol penetrates beyond the volume at which airways involved in asthmaoccur, trapping of the aerosol will be seen. This trapping phenomenawill be demonstrated by the presence of aerosol in subsequentexhalations after the inhalation of the bolus. Thus, using the method ofthe present invention, the diagnosis of asthma can be based upon thepresence of aerosol in exhalations where no aerosol was introduced onthe inhalation portion of that breathing cycle and subsequent to theintroduction of aerosol in a prior inhalation. The lowest volume ofpenetration at which this trapping is seen to initially occur designatesthe volume at which therapeutic aerosol should be introduced foralleviation of the symptoms of asthma.

Pharmaceutical active agents can also be delivered with the apparatus ofthe invention. In the preferred embodiment, the active agent iscontained in the aerosol generator, and is released with the aerosol.The release of the active agent with the aerosol at the determined pointof the breathing cycle helps to ensure that the active agent isdelivered to the region of obstruction or inflammation in the lung asdetermined by the apparatus and method of the invention. Knowledge ofthe volume of penetration of the aerosol bolus provides the necessaryinformation to deliver the active agent at the obstruction site.

It is to be understood that other embodiments may be utilized andstructural changes may be made without departing from the scope of thepresent invention.

1.-15. (canceled)
 16. A method for treating an obstruction in the upperregion of the lungs, the method comprising: a. measuring pressure dataand calculating volume of airflow of a breathing cycle; b. providing avolume of penetration; c. providing an aerosol bolus at a determinedpoint of the breathing cycle; d. measuring a concentration values ofaerosol particles and calculating time constants from the measuredaerosol concentration values; e. repeating steps b to d using adifferent volume of penetration; f. comparing the calculated timeconstants, in a processing device, from at least two provided volumes ofpenetration to determine the position of an obstruction; and g.releasing a treatment bolus at a select point of the breathing cyclewhich is chosen based upon the determined position of the obstruction.17. The method of claim 16, wherein the select point is chosen toconcentrate the treatment bolus in a selected volume of air flowdetermined to contact the position of the obstruction during thebreathing cycle.
 18. The method of claim 16, wherein the treatment boluscomprises an active pharmaceutical.
 19. A method for treating anobstruction in the upper region of the lungs, the method comprising: a.measuring pressure data and calculating volume of airflow of a breathingcycle; b. providing a volume of penetration; c. providing an aerosolbolus at a determined point of the breathing cycle; d. measuring aconcentration values of aerosol particles and calculating time constantsfrom the measured aerosol concentration values; e. repeating steps b tod using a different volume of penetration; f. comparing the calculatedtime constants, in a processing device, from at least two providedvolumes of penetration to determine the position of inflammation; and g.releasing a treatment bolus at a select point of the breathing cyclewhich is chosen based upon the determined position of the inflammation.20. The method of claim 19, wherein the select point is chosen toconcentrate the treatment bolus in a selected volume of air flowdetermined to contact the position of the inflammation during thebreathing cycle.
 21. The method of claim 19, wherein the treatment boluscomprises a bronchial dilating agent.
 22. The method of claim 19,wherein the treatment bolus comprises an active pharmaceutical.